An extension problem for convex functions

TL;DR

This paper investigates conditions under which convex functions defined on a linear subspace can be extended to the entire space with controlled estimates, inspired by analogous results in metric extension theory.

Contribution

It introduces a new extension theorem for convex functions with estimates, inspired by metric extension results for positive line bundles.

Findings

Established a new extension criterion for convex functions

Provided estimates for the extended functions

Linked convex function extension to metric extension theory

Abstract

We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles